Click here to load reader

ESE 570: Digital Integrated Circuits and VLSI Fundamentals ese570/spring2019/handouts/lec12.pdf · PDF file nMOS 1st Order RC Delay Model – Equiv. R n 3 R n = R un / ... Super-Buffer

  • View
    18

  • Download
    1

Embed Size (px)

Text of ESE 570: Digital Integrated Circuits and VLSI Fundamentals...

  • ESE 570: Digital Integrated Circuits and VLSI Fundamentals

    Lec 12: February 26, 2019 Interconnect Delay

    Penn ESE 570 Spring 2019 – Khanna

  • Lecture Outline

    !  1st Model Reminder !  Driving Large Loads !  Interconnect Delay

    2 Penn ESE 570 Spring 2019 – Khanna

  • nMOS 1st Order RC Delay Model – Equiv. Rn

    3

    Rn = Run/κn

    κnCg

    κnCd

    κnCd

    κn ON/ OFF

    Penn ESE 570 Spring 2019 – Khanna

    Rp = Rup/κp

    κpCg

    κpCd

    κpCd

    κp ON/OFF

    d

    s

  • 1st Order Delay Model -τPHL

    4

    κp κp

    1 1 A Y

    VDD VDD

    where Wn=Wunit => κn=1, Rn=Run Wp = κpWunit

    κp = µn/ µp = 2

    Rp = Rup/κp = Rn

    1,κp

    1,κp

    1,κp n

    2

    1

    Penn ESE 570 Spring 2019 – Khanna

    VDD VDD

    κpCd nκpC

    g

    κnC κnC

    Rn/n Rn Cd nCg

    Y

    Cload = (1 + κp)(Cd + nCg)

    τ PHL ≈ 0.69RnCload = 0.69Rn (1+κ p )(Cd + nCg )

    τ PHL = τ PLH

  • Large Fanout Delay

    !  What is delay if must drive fanout=100?

    Penn ESE 570 Spring 2019 - Khanna 5

  • …and Again

    !  Delay here?

    Penn ESE 570 Spring 2019 - Khanna 6

  • Super-Buffer to Drive Large CLOAD

    7

    INV1

    Stage-0

    a -> stage scale factor > 1

    NOTE for CMOS INV: Cd = Cdbn + Cdbp Cg = Cgbn + Cgbp

    CLOAD

    Penn ESE 570 Spring 2019 – Khanna

  • Super-Buffer to Drive Large CLOAD

    8

    INV1

    Stage-0

    a -> stage scale factor > 1

    Wni = a iWn0, Lni = Ln0 and Wpi = a

    iWp0, Lpi = Lp0 for i = 0, 1, 2, ..., N

    NOTE for CMOS INV: Cd = Cdbn + Cdbp Cg = Cgbn + Cgbp

    CLOAD

    Penn ESE 570 Spring 2019 – Khanna

  • Super-Buffer to Drive Large CLOAD

    9

    INV1

    Stage-0

    a -> stage scale factor > 1

    Wni = a iWn0, Lni = Ln0 and Wpi = a

    iWp0, Lpi = Lp0 for i = 0, 1, 2, ..., N

    Stage load capacitances Cloadi are also scaled by a

    Cloadi = a i Cload0 = a

    i (Cd + aCg) for i = 0, 1, 2, .., N

    NOTE for CMOS INV: Cd = Cdbn + Cdbp Cg = Cgbn + Cgbp

    CLOAD

    Penn ESE 570 Spring 2019 – Khanna

  • Super-Buffer to Drive Large CLOAD

    10

    INV1

    Stage-0

    a -> stage scale factor > 1

    Wni = a iWn0, Lni = Ln0 and Wpi = a

    iWp0, Lpi = Lp0 for i = 0, 1, 2, ..., N

    Stage load capacitances Cloadi are also scaled by a

    Cloadi = a i Cload0 = a

    i (Cd + aCg) for i = 0, 1, 2, .., N when i = N: CloadN = a

    N Cload0 = a N (Cd + aCg)

    NOTE for CMOS INV: Cd = Cdbn + Cdbp Cg = Cgbn + Cgbp

    CLOAD

    Penn ESE 570 Spring 2019 – Khanna

  • Super-Buffer to Drive Large CLOAD

    11

    INV1

    Stage-0

    a -> stage scale factor > 1

    Wni = a iWn0, Lni = Ln0 and Wpi = a

    iWp0, Lpi = Lp0 for i = 0, 1, 2, ..., N

    Stage load capacitances Cloadi are also scaled by a

    Cloadi = a i Cload0 = a

    i (Cd + aCg) for i = 0, 1, 2, .., N when i = N: CloadN = a

    N Cload0 = a N (Cd + aCg) => let CLOAD = a

    N(aCg) = a N+1Cg

    NOTE for CMOS INV: Cd = Cdbn + Cdbp Cg = Cgbn + Cgbp

    CLOAD

    Penn ESE 570 Spring 2019 – Khanna

  • Super-Buffer to Drive Large CLOAD

    12

    INV1

    Stage-0

    a -> stage scale factor > 1

    Wni = a iWn0, Lni = Ln0 and Wpi = a

    iWp0, Lpi = Lp0 for i = 0, 1, 2, ..., N

    Stage load capacitances Cloadi are also scaled by a

    Cloadi = a i Cload0 = a

    i (Cd + aCg) for i = 0, 1, 2, .., N when i = N: CloadN = a

    N Cload0 = a N (Cd + aCg) => let CLOAD = a

    N(aCg) = a N+1Cg

    CLOAD/Cg = a N+1 =>

    NOTE for CMOS INV:

    N is rounded up to nearest integer value.

    Cd = Cdbn + Cdbp Cg = Cgbn + Cgbp

    CLOAD

    N = ln(CLOAD Cg )

    lna −1

    Penn ESE 570 Spring 2019 – Khanna

  • 13

    NOTE: ALL inverters Stage-0 through Stage-N have the same gate delay

    CLOAD

    CLOAD

    τ p = τ PHL +τ PLH

    2 = Γ

    Cload W

    Super-Buffer to Drive Large CLOAD

    Penn ESE 570 Spring 2019 – Khanna

  • 14

    NOTE: ALL inverters Stage-0 through Stage-N have the same gate delay

    Let τ0 = gate delay for INV1 (with a = 1) with load Cload = Cd + Cg

    CLOAD

    CLOAD

    τ p = τ PHL +τ PLH

    2 = Γ

    Cload W

    Super-Buffer to Drive Large CLOAD

    Penn ESE 570 Spring 2019 – Khanna

  • 15

    NOTE: ALL inverters Stage-0 through Stage-N have the same gate delay

    Let τ0 = gate delay for INV1 (with a = 1) with load Cload = Cd + Cg

    CLOAD

    CLOAD

    τ p = τ PHL +τ PLH

    2 = Γ

    Cload W

    Super-Buffer to Drive Large CLOAD

    τ p0 τ 0

    = Cload0 W0

    (Cd +Cg ) W0 = Cd + aCg Cd +Cg

    ⇒ τ p0 = τ 0 Cd + aCg Cd +Cg

    For Stage-0:

    Penn ESE 570 Spring 2019 – Khanna

  • 16

    NOTE: ALL inverters Stage-0 through Stage-N have the same gate delay

    Let τ0 = gate delay for INV1 (with a = 1) with load Cload = Cd + Cg

    CLOAD

    CLOAD

    τ p = τ PHL +τ PLH

    2 = Γ

    Cload W

    Super-Buffer to Drive Large CLOAD

    τ p0 τ 0

    = Cload0 W0

    (Cd +Cg ) W0 = Cd + aCg Cd +Cg

    ⇒ τ p0 = τ 0 Cd + aCg Cd +Cg

    For Stage-0:

    Penn ESE 570 Spring 2019 – Khanna

  • 17

    CLOAD

    CLOAD

    Super-Buffer to Drive Large CLOAD

    τ p0 τ 0

    = Cload0 W0

    (Cd +Cg ) W0 = Cd + aCg Cd +Cg

    ⇒ τ p0 = τ 0 Cd + aCg Cd +Cg

    For Stage-0:

    Penn ESE 570 Spring 2019 – Khanna

  • 18

    CLOAD

    CLOAD

    Super-Buffer to Drive Large CLOAD

    τ p0 τ 0

    = Cload0 W0

    (Cd +Cg ) W0 = Cd + aCg Cd +Cg

    ⇒ τ p0 = τ 0 Cd + aCg Cd +Cg

    For Stage-0:

    For Stage-1: τ p1 τ 0

    = Cload1 aW0 (Cd +Cg ) W0

    = aCd + a

    2Cg( ) / a Cd +Cg

    ⇒ τ p1 = τ 0 Cd + aCg Cd +Cg

    = τ p0

    Penn ESE 570 Spring 2019 – Khanna

  • 19

    CLOAD

    CLOAD

    Super-Buffer to Drive Large CLOAD

    τ p0 τ 0

    = Cload0 W0

    (Cd +Cg ) W0 = Cd + aCg Cd +Cg

    ⇒ τ p0 = τ 0 Cd + aCg Cd +Cg

    For Stage-0:

    For Stage-1: τ p1 τ 0

    = Cload1 aW0 (Cd +Cg ) W0

    = aCd + a

    2Cg( ) / a Cd +Cg

    ⇒ τ p1 = τ 0 Cd + aCg Cd +Cg

    = τ p0

    Penn ESE 570 Spring 2019 – Khanna

  • 20

    CLOAD

    CLOAD

    Super-Buffer to Drive Large CLOAD

    τ p0 τ 0

    = Cload0 W0

    (Cd +Cg ) W0 = Cd + aCg Cd +Cg

    ⇒ τ p0 = τ 0 Cd + aCg Cd +Cg

    For Stage-0:

    For Stage-1:

    For Stage-N:

    τ p1 τ 0

    = Cload1 aW0 (Cd +Cg ) W0

    = aCd + a

    2Cg( ) / a Cd +Cg

    ⇒ τ p1 = τ 0 Cd + aCg Cd +Cg

    = τ p0

    τ pN τ 0

    = CloadN a

    NW0 (Cd +Cg ) W0

    = aNCd + a

    N+1Cg( ) / aN Cd +Cg

    ⇒ τ pN = τ 0 Cd + aCg Cd +Cg

    = τ p0

    Penn ESE 570 Spring 2019 – Khanna

  • 21

    CLOAD

    CLOAD

    Super-Buffer to Drive Large CLOAD

    τ p0 τ 0

    = Cload0 W0

    (Cd +Cg ) W0 = Cd + aCg Cd +Cg

    ⇒ τ p0 = τ 0 Cd + aCg Cd +Cg

    For Stage-0:

    For Stage-1:

    For Stage-N:

    τ p1 τ 0

    = Cload1 aW0 (Cd +Cg ) W0

    = aCd + a

    2Cg( ) / a Cd +Cg

    ⇒ τ p1 = τ 0 Cd + aCg Cd +Cg

    = τ p0

    τ pN τ 0

    = CloadN a

    NW0 (Cd +Cg ) W0

    = aNCd + a

    N+1Cg( ) / aN Cd +Cg

    ⇒ τ pN = τ 0 Cd + aCg Cd +Cg

    = τ p0

    τ total = (N +1)τ p0 = (N +1)τ 0 Cd + aCg Cd +Cg

    Penn ESE 570 Spring 2019 – Khanna

  • 22

    CLOAD

    CLOAD

    Super-Buffer to Drive Large CLOAD

    τ p0 τ 0

    = Cload0 W0

    (Cd +Cg ) W0 = Cd + aCg Cd +Cg

    ⇒ τ p0 = τ 0 Cd + aCg Cd +Cg

    For Stage-0:

    For Stage-1:

    For Stage-N:

    τ p1 τ 0

    = Cload1 aW0 (Cd +Cg ) W0

    = aCd + a

    2Cg( ) / a Cd +Cg

    ⇒ τ p1 = τ 0 Cd + aCg Cd +Cg

    = τ p0

    τ pN τ 0

    = CloadN a

    NW0 (Cd +Cg ) W0

    = aNCd + a

    N+1Cg( ) / aN Cd +Cg

    ⇒ τ pN = τ 0 Cd + aCg Cd +Cg

    = τ p0

    τ total = (N +1)τ p0 = (N +1)τ 0 Cd + aCg Cd +Cg

    Choose N and a to minimize τtotal Penn ESE 570 Spring 2019 – Khanna

  • Super-Buffer to Drive Large CLOAD

    23

    τ total = (N +1)τ p0 = (N +1)τ 0 Cd + aCg Cd +Cg

    N = ln(CLOAD Cg )

    lna −1

    τ total = ln(CLOAD Cg )

    lna τ 0 Cd + aCg Cd +Cg

    Penn ESE 570 Spring 2019 – Khanna

  • Super-Buffer to Drive Large CLOAD

    24

    TO MINIMIZE τto

Search related